Many newly synthesized cellular proteins pass through the Golgi complex from where secretory transport carriers sort them to the plasma membrane and the extracellular environment. The formation of these secretory carriers at the trans-Golgi network is promoted by the protein kinase D (PKD) family of serine/threonine kinases. Here, using mathematical modeling and experimental validation of the PKD activation and substrate phosphorylation kinetics, we reveal that the expression level of the PKD substrate deleted in liver cancer 1 (DLC1), a Rho GTPase-activating protein that is inhibited by PKD-mediated phosphorylation, determines PKD activity at the Golgi membranes. RNAi-mediated depletion of DLC1 reduced PKD activity in a Rho-Rho-associated protein kinase (ROCK)-dependent manner, impaired the exocytosis of the cargo protein horseradish peroxidase, and was associated with the accumulation of the small GTPase RAB6 on Golgi membranes, indicating a protein-trafficking defect. In summary, our findings reveal that DLC1 maintains basal activation of PKD at the Golgi and Golgi secretory activity, in part by down-regulating Rho-ROCK signaling. We propose that PKD senses cytoskeletal changes downstream of DLC1 to coordinate Rho signaling with Golgi secretory function.

BACKGROUND:In mammalian cells protein-lipid interactions at the trans-Golgi network (TGN) determine the formation of vesicles, which transfer secretory proteins to the cellular membrane. This process is regulated by a complex molecular network including protein kinase D (PKD), which is directly involved in the fission of transport vesicles, and its interaction with the ceramide transfer protein CERT that transports ceramide from the endoplasmic reticulum to the TGN.RESULTS:Here we present a novel quantitative kinetic model for the interactions of the key players PKD, phosphatidylinositol 4-kinase III beta (PI4KIII β) and CERT at the TGN membranes. We use sampling-based Bayesian analysis and perturbation experiments for model calibration and validation.CONCLUSIONS:Our quantitative predictions of absolute molecular concentrations and reaction fluxes have major biological implications: Model comparison provides evidence that PKD and CERT interact in a cooperative manner to regulate ceramide transfer. Furthermore, we identify active PKD to be the dominant regulator of the network, especially of CERT-mediated ceramide transfer.

Here we present a minimal mathematical model for the sphingomyelin synthase 1 (SMS1) driven conversion of ceramide to sphingomyelin based on chemical reaction kinetics. We demonstrate via mathematical analysis that this model is not able to qualitatively reproduce experimental measurements on lipid compositions after altering SMS1 activity. We prove that a positive feedback mechanism from the products to the reactants of the reaction is one possible model extension to explain these specific experimental data. The proposed mechanism in fact exists in vivo via protein kinase D and the ceramide transfer protein CERT. The model is further evaluated by additional observations from the literature.

Motivation: Experiment design strategies for biomedical models with the purpose of parameter estimation or model discrimination are in the focus of intense research. Experimental limitations such as sparse and noisy data result in unidentifiable parameters and render-related design tasks challenging problems. Often, the temporal resolution of data is a limiting factor and the amount of possible experimental interventions is finite. To address this issue, we propose a Bayesian experiment design algorithm to minimize the prediction uncertainty for a given set of experiments and compare it to traditional A-optimal design. Results: In an in depth numerical study involving an ordinary differential equation model of the trans-Golgi network with 12 partly non-identifiable parameters, we minimized the prediction uncertainty efficiently for predefined scenarios. The introduced method results in twice the prediction precision as the same amount of A-optimal designed experiments while introducing a useful stopping criterion. The simulation intensity of the algorithm's major design step is thereby reasonably affordable. Besides smaller variances in the predicted trajectories compared with Fisher design, we could also achieve smaller parameter posterior distribution entropies, rendering this method superior to A-optimal Fisher design also in the parameter space. Availability: Necessary software/toolbox information are available in the supplementary material. The project script including example data can be downloaded from http://www.ist.uni-stuttgart.de/%7eweber/BayesFisher2012. Contact: patrick.weber@ist.uni-stuttgart.de Supplementary Information: Supplementary data are available at Bioinformatics online.

Understanding cellular regulation processes at a molecular and systems level requires quantitative dynamic modeling approaches. Systems of ordinary differential equations are commonly used for this purpose. The inverse problem to estimate parameters of these models from experimental data unfortunately poses several challenges, e.g. concerning computational costs and identifiability issues. In this paper we focus on a maximum likelihood based approach for parameter estimation from relative measurement data, meaning that the model outputs are proportional to internal model states but the proportionality factors are unknown. We introduce a novel method to reduce the dimensionality of the respective optimization problem and to solve it efficiently. Furthermore, the method of profile likelihoods is established to study the reliability of point estimates and identifiability problems which arise then considering relative instead of absolute data. Our approaches are evaluated using two biological network models.